Related papers: On computing the total displacement number via wei…

We consider the problem of tracking one solution path defined by a polynomial homotopy on a parallel shared memory computer. Our robust path tracker applies Newton's method on power series to locate the closest singular parameter value. On…

Mining movement data to reveal interesting behavioral patterns has gained attention in recent years. One such pattern is the convoy pattern which consists of at least m objects moving together for at least k consecutive time instants where…

We count the number of walks of length n on a k-node circular digraph that cover all k nodes in two ways. The first way illustrates the transfer-matrix method. The second involves counting various classes of height-restricted lattice paths.…

We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average…

So called $S$-Motzkin paths are combined the concepts `catastrophes' and `air pockets. The enumeration is done by properly set up bivariate generating functions which can be extended using the kernel method.

The aim of this paper is to justify in dimensions two and three the ansatz of Caracciolo et al. stating that the displacement in the optimal matching problem is essentially given by the solution to the linearized equation i.e. the Poisson…

The problem of motion for different test particles, charged and spinning objects of constant spinning tensor in different versions of bimetric theory of gravity is obtained by deriving their corresponding path and path deviation equations,…

Given the set of paths through a digraph, the result of uniformly deleting some vertices and identifying others along each path is coherent in such a way as to yield the set of paths through another digraph, called a \emph{path abstraction}…

This paper addresses the problem of finding shortest paths homotopic to a given disjoint set of paths that wind amongst point obstacles in the plane. We present a faster algorithm than previously known.

A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…

We introduce a new concept of permutation avoidance pattern called hatted pattern, which is a natural generalization of the barred pattern. We show the growth rate of the class of permutations avoiding a hatted pattern in comparison to…

Clustering is one of the fundamental tasks in data analytics and machine learning. In many situations, different clusterings of the same data set become relevant. For example, different algorithms for the same clustering task may return…

In this paper I investigate several offline and online data transfer scheduling problems and propose efficient algorithms and techniques for addressing them. In the offline case, I present a novel, heuristic, algorithm for scheduling files…

We describe an algorithm, implemented in Python, which can enumerate any permutation class with polynomial enumeration from a structural description of the class. In particular, this allows us to find formulas for the number of permutations…

Saddle-point problems appear in various settings including machine learning, zero-sum stochastic games, and regression problems. We consider decomposable saddle-point problems and study an extension of the alternating direction method of…

Human mobility describes physical patterns of movement of people within a spatial system. Many of these patterns, including daily commuting, are cyclic and quantifiable. These patterns capture physical phenomena tied to processes studied in…

This paper considers a multi-patch model, where each patch follows a logistic law, and patches are coupled by asymmetrical migration terms. First, in the case of perfect mixing, i.e when the migration rate tends to infinity, the total…

We propose an experimental mathematics approach leading to the computer-driven discovery of various structural properties of general counting functions coming from enumeration of walks.

Many applications modeled by polynomial systems have positive dimensional solution components (e.g., the path synthesis problems for four-bar mechanisms) that are challenging to compute numerically by homotopy continuation methods. A…

The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement…